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International Olympiad of metropolises 2016 P3

Source: International olympiad of metropolises 2016

September 7, 2016
IOMalgebrageometry

Problem Statement

Let A1A2...AnA_1A_2 . . . A_n be a cyclic convex polygon whose circumcenter is strictly in its interior. Let B1,B2,...,BnB_1, B_2, ..., B_n be arbitrary points on the sides A1A2,A2A3,...,AnA1A_1A_2, A_2A_3, ..., A_nA_1, respectively, other than the vertices. Prove that B1B2A1A3+B2B3A2A4+...+BnB1AnA2>1\frac{B_1B_2}{A_1A_3}+ \frac{B_2B_3}{A_2A_4}+...+\frac{B_nB_1}{A_nA_2}>1.
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